Relationship of second order susceptibility to the dimensions of ZnO nanorods based on Lorentz local field

With the aid of Maker fringe technique, we have observed two nonlinear optical (NLO) phenomena separately on diameter and length of ZnO nanorod (NR). One is second harmonic generation (SHG) saturation in rod diameter, and the other is SHG enhancement in rod length. Besides that, the model based on Lorentz local field is proposed for the first time to elucidate the above phenomena. The deduced second order susceptibility χ (2) with various sizes of ZnO NR matches well to our theory, demonstrating that the size effect on χ (2) is governed by Lorentz local field. Our theory provides a theoretical basis to explain the mechanism of light-material interaction in nano-dimensions and is readily to be extended to other kind of semiconductor nanostructures when addressing NLO properties in them.